1. LaTasha has started her own custom T-Shirt company, T\'s T\'s, which produces silk screened T-shirts for various occasions and organizations; as well as a brisk walk-in trade. Her shop is located in a small beach community in Florida. Since she has just started she is renting the equipment from a large firm in Jacksonville. The cost of renting the equipment is $500. The material used in one custom T-shirt costs $4.50, and LaTasha is selling the T-shirts for $12 each. a. If LaTasha sells 50 shirts, 1. What will her total revenue be? 2. What will her total cost be? b. How many shirts must LaTasha sell to break even? c. What is the total revenue at the break-even point? Solution 1. The total revenue is equal to the amount of income gained by selling the 50 shirts, not accounting for any expenses (which net profit or net income values take into account). The T- shirts are sold for $12 each, so one T-shirt costs $12, two T-shirts cost 2 times $12 = $24, and so on. If 50 T-shirts are sold: Total Revenue = (50 T-shirts) ($12 per T-shirt) = $600 2. Her total cost is equal to the amount she has to pay. First, she must rent equipment for $500, which she pays, and she must also pay $4.50 for each T-shirt that she buys (and may or may not sell). Her total cost is the sum of the costs of the equipment and the T-shirts: Total Cost = $500 + (50 T-shirts) ($4.50 per T-shirt) = $500 + $225 = $725 b) In order to break even, the total revenue must equal the total cost. If x is the number of T- shirts needed for LaTasha to break even, her total revenue must equal her total cost. Her total revenue is given by 12x ($12 per each T-shirt), and her total cost is given by 500 + 4.50x ($500 rent plus $4.50 per each T-shirt). We want to solve for x when the total revenue and total cost are equal: Total Revenue = Total Cost 12x = 500 + 4.50x 7.50x = 500 x = 500/7.50 = 66.66666... 67 T-shirts c) After breaking even, her total revenue, given by 12x, is found by multiplying 12 by the value of x we just calculated: x 67 Total Revenue = 12x = 12 (67) = $804 (Note that, because we can\'t sell 0.666... of a T-shirt, x is rounded to 67 T-shirts. However, when x = 67, the total revenue actually exceeds the total cost by a bit, so it isn\'t exactly \"breaking even\", but its as close as possible that we can get while still selling an integer number of T-shirts.).